$15,000 is only the maximum before you have to file a Gift Tax return. However, no gift taxes are usually due

No deduction but but no tax liability either. 

You have no tax liability (and no deduction) for the gifts to your children. You don't even report the gifts anywhere. But you do have to report the sale of the stock. If you had a gain (profit) from the sale, you might have to pay tax on the gain.

Why no capital gains tax? Or did you mean the kids don't have to pay taxes on the gift?

Yes, capital gains would be taxed.  I was thinking the stock was given as a gift in which case there would not have been any capital gains.